Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2025-2pp.1289-1313

Archive of Issues

Total articles in the database: 13205
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8140
In English (Mech. Solids): 5065

<< Previous article | Volume 60, Issue 2 / 2025 | Next article >>
Saurav Sharma, Sangeeta Devi, Rajneesh Kumar, Ibrahim S. Elshazly, Imed Bachar, and Kh. Lotfy, "Investigation of Uniqueness, Reciprocity Theorems and Deformation in Multi-Phase-Lags Anisotropic Thermoviscoelastic Diffusion Model," Mech. Solids. 60 (2), 1289-1313 (2025)
Year 2025 Volume 60 Number 2 Pages 1289-1313
DOI 10.1134/S0025654425600242
Title Investigation of Uniqueness, Reciprocity Theorems and Deformation in Multi-Phase-Lags Anisotropic Thermoviscoelastic Diffusion Model
Author(s) Saurav Sharma (University of Houston Cullen College of Engineering, Houston, Texas, 77054 USA, University of Houston Cullen College of Engineering, Houston, Texas, 77054 USA, sauravkuk@gmail.com)
Sangeeta Devi (Salarpura (Gheer), Karnal, Haryana, India, pin-132023, Salarpura (Gheer), Karnal, Haryana, 132023 India, sangeetakamboz@gmail.com)
Rajneesh Kumar (Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India, rajneesh_kuk@rediffmail.com)
Ibrahim S. Elshazly (Department of Basic Sciences, Common First Year, King Saud University, Riyadh, 11451 Saudi Arabia, iali2.c@ksu.edu.sa)
Imed Bachar (Department of Mathematics, College of Science, King Saud University, Riyadh, 11451 Saudi Arabia, abachar@ksu.edu.sa)
Kh. Lotfy (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt, khlotfy_1@yahoo.com)
Abstract A new model involving the equations of thermoviscoelastic diffusion under multi-phase-lags for anisotropic medium (ATDM) is presented. The simulated model is obtained after modifying the basic Fourier’s [1] and Fick’s [2] laws to involve the higher order time derivatives of heat flow vector, the gradient of temperature, diffusing mass flux, and chemical potential gradient. The governing equations for the ATDM are considered to establish uniqueness and reciprocity theorems. By applying the Laplace transform a uniqueness theorem for the considered model is proved and the reciprocity theorem is derived. Instantaneous concentrated body forces, heat sources, and chemical potential sources along with moving heat and chemical potential sources are taken to illustrate the applications of the reciprocity theorem for a specific case. It has been recognized that these theorems are impacted by the perceptivity of the involved field variable along with the variations of parameters involving higher-order time derivatives. Also, the orthotropic thermoviscoelastic diffusion with a multi-phase-lags model for the one-dimensional case presents a deformation due to thermal and chemical potential sources. As the application of the problem instantaneous thermal and instantaneous chemical potential sources are taken. Comparison has been made for Lord-Shulman (LS), dual phase lags, and higher order time derivatives on displacement, stress, temperature, and chemical potential. Some unique cases are also established and correlated with known results. The effect of phase-lags plays an important role in processing and characterization to improve material properties and find applications in geomechanics, earthquake engineering, and the designing of new materials.
Keywords thermoviscoelastic, diffusion, anisotropic, multi-phase-lags, uniqueness, reciprocity theorem, and deformation
Received 18 January 2025Revised 15 February 2025Accepted 26 February 2025
Link to Fulltext
<< Previous article | Volume 60, Issue 2 / 2025 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100